Modelwriting.ipynb

Kernel: SageMath (stable)

var('l m h t')

(l, m, h, t)

P=1000
k1=.5
k2=.4
k3=.1
F= [P-(k2*m+k3*h),P-(k1*l+k3*h),P-(k1*l+k2*m)]
times=(0,10,1)
soln=desolve_odeint(F,[0,0],times,[l,m,h])

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-5-3f6f467b1467> in <module>()
      5 F= [P-(k2*m+k3*h),P-(k1*l+k3*h),P-(k1*l+k2*m)]
      6 times=(Integer(0),Integer(10),Integer(1))
----> 7 soln=desolve_odeint(F,[Integer(0),Integer(0)],times,[l,m,h])

/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/calculus/desolvers.pyc in desolve_odeint(des, ics, times, dvars, ivar, compute_jac, args, rtol, atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg)
   1565     sol=odeint(func, ics, times, args=args, Dfun=Dfun, rtol=rtol, atol=atol,
   1566         tcrit=tcrit, h0=h0, hmax=hmax, hmin=hmin, ixpr=ixpr, mxstep=mxstep,
-> 1567         mxhnil=mxhnil, mxordn=mxordn, mxords=mxords, printmessg=printmessg)
   1568 
   1569     return sol
/ext/sage/sage-8.1/local/lib/python2.7/site-packages/scipy/integrate/odepack.pyc in odeint(func, y0, t, args, Dfun, col_deriv, full_output, ml, mu, rtol, atol, tcrit, h0, hmax, hmin, ixpr, mxstep, mxhnil, mxordn, mxords, printmessg)
    213     output = _odepack.odeint(func, y0, t, args, Dfun, col_deriv, ml, mu,
    214                              full_output, rtol, atol, tcrit, h0, hmax, hmin,
--> 215                              ixpr, mxstep, mxhnil, mxordn, mxords)
    216     if output[-1] < 0:
    217         warning_msg = _msgs[output[-1]] + " Run with full_output = 1 to get quantitative information."
/ext/sage/sage-8.1/local/lib/python2.7/site-packages/sage/calculus/desolvers.pyc in func(y, t)
   1549             v = list(y[:])
   1550             v.append(t)
-> 1551             return [dec(*v) for dec in desc]
   1552 
   1553         if not compute_jac:
/ext/sage/sage-8.1/src/sage/ext/interpreters/wrapper_rdf.pyx in sage.ext.interpreters.wrapper_rdf.Wrapper_rdf.__call__ (build/cythonized/sage/ext/interpreters/wrapper_rdf.c:2111)()
     69 
     70     def __call__(self, *args):
---> 71         if self._n_args != len(args): raise ValueError
     72         cdef double* c_args = self._args
     73         cdef int i
ValueError: 

The model dp/dt=rp(1-p/N)-ep represents the population of horses on an island. The parameter p respresent the the orginal starting population of the horses, while the N represents the the max amounnt of horses the enviroment can handle. The r and e are variables that are related to the parameter p.

var('t v y')
g = 9.81
k= 0.47
m=1
F = [v,-g-k/m*abs(v)*v]
times=srange(0,4,0.1)
soln=desolve_odeint(F,[0,20],times,[y,v])

velocity=zip(times,[x[1] for x in soln])

line(velocity,axes_labels=['time','velocity'])